I think that's a severe misrepresentation of China. They're communist in name, but extremely capitalist in practice. Jack Ma is the man behind Alibaba and now one of the richest people alive, let alone Chinese alive. Check out his background [1].
In my opinion, the main difference between China and the US is nationalism. And that's also what I think that slogan is indicative of. It also, I think, explains their government actions. Supporting their companies is not about nationalizing them, which implies a motivation of state driven control, but growing and improving Chinese companies on the national scene.
I think we have a great analogy in the US today versus the US in the past. Think about our space program in the 60s. We dumped immense amount of money into US companies and managed to, in 7 years, go from having never even put a man into orbit to putting a man on the moon. The primary motivation there was nationalistic - showing how kick ass America, and implicitly capitalism, was.
Compare that space program to today where there's no real nationalism. Now a days we're building the Space Shuttle 2.0, known as the SLS. And we've spent 8 years on it so far, obscene amounts of money, and it's still not going anywhere. The thing is now the motivation for the spending is not about America, but about a handful of congressmen using it as a job's program for their election campaigns, and of course shelling out kickbacks everywhere. If we handed out a fraction of the SLS money to a private company like SpaceX we'd have a man on Mars in the 2020s, but again - the goal is no longer about America or space. It's become about the individual, instead of the nation.
So essentially I think China's goal here is not state control, but about showing dominance of the Chinese system. If there is any problem with the American system it's that I think we've become somewhat conservative with ideas. Elon Musk's ideas should not be as unique as they are. I mean they aren't - everybody has them, but funding for revolutionary ideas seems (based on the lack of these sort of companies) to be much more difficult to come by. Ostensibly it makes sense. Investors want to invest in things likely to turn a profit, and investing in something that's never been done before is not the easiest EV to predict. But with our technology and wealth today we could be doing so many much more interesting things than we are.
[1] - https://en.wikipedia.org/wiki/Jack_Ma